5x^2-175x+140=0

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Solution for 5x^2-175x+140=0 equation: 


Simplifying
5x2 + -175x + 140 = 0

Reorder the terms:
140 + -175x + 5x2 = 0

Solving
140 + -175x + 5x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5'.
5(28 + -35x + x2) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(28 + -35x + x2)' equal to zero and attempt to solve:

Simplifying
28 + -35x + x2 = 0

Solving
28 + -35x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-28' to each side of the equation.
28 + -35x + -28 + x2 = 0 + -28

Reorder the terms:
28 + -28 + -35x + x2 = 0 + -28

Combine like terms: 28 + -28 = 0
0 + -35x + x2 = 0 + -28
-35x + x2 = 0 + -28

Combine like terms: 0 + -28 = -28
-35x + x2 = -28

The x term is -35x.  Take half its coefficient (-17.5).
Square it (306.25) and add it to both sides.

Add '306.25' to each side of the equation.
-35x + 306.25 + x2 = -28 + 306.25

Reorder the terms:
306.25 + -35x + x2 = -28 + 306.25

Combine like terms: -28 + 306.25 = 278.25
306.25 + -35x + x2 = 278.25

Factor a perfect square on the left side:
(x + -17.5)(x + -17.5) = 278.25

Calculate the square root of the right side: 16.680827318

Break this problem into two subproblems by setting 
(x + -17.5) equal to 16.680827318 and -16.680827318.


Subproblem 1
x + -17.5 = 16.680827318

Simplifying
x + -17.5 = 16.680827318

Reorder the terms:
-17.5 + x = 16.680827318

Solving
-17.5 + x = 16.680827318

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '17.5' to each side of the equation.
-17.5 + 17.5 + x = 16.680827318 + 17.5

Combine like terms: -17.5 + 17.5 = 0.0
0.0 + x = 16.680827318 + 17.5
x = 16.680827318 + 17.5

Combine like terms: 16.680827318 + 17.5 = 34.180827318
x = 34.180827318

Simplifying
x = 34.180827318


Subproblem 2
x + -17.5 = -16.680827318

Simplifying
x + -17.5 = -16.680827318

Reorder the terms:
-17.5 + x = -16.680827318

Solving
-17.5 + x = -16.680827318

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '17.5' to each side of the equation.
-17.5 + 17.5 + x = -16.680827318 + 17.5

Combine like terms: -17.5 + 17.5 = 0.0
0.0 + x = -16.680827318 + 17.5
x = -16.680827318 + 17.5

Combine like terms: -16.680827318 + 17.5 = 0.819172682
x = 0.819172682

Simplifying
x = 0.819172682


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {34.180827318, 0.819172682}
Solution
x = {34.180827318, 0.819172682}

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